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An Analytic Approach for Calculating Absolutely Unstable Inviscid Modes of the Boundary Layer on a Rotating Disk
Author(s) -
Turkyilmazoglu M.,
Gajjar J. S. B.
Publication year - 2001
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00173
Subject(s) - inviscid flow , instability , boundary layer , wavenumber , rayleigh scattering , mathematical analysis , physics , mathematics , boundary (topology) , boundary value problem , mechanics , classical mechanics , optics
An analytical treatment of inviscidly absolutely unstable modes is pursued using the long‐wavelength asymptotic approach. It is shown using the inviscid Rayleigh scalings in conjunction with the linear critical layer theory that the rotating‐disk boundary layer flow undergoes a region of absolute instability for some small azimuthal wave numbers. The analytically calculated branch points for the absolute instability are found to be in good agreement with those obtained via a numerical solution of the inviscid Rayleigh equation.